WASHINGTON — A bipartisan Senate proposal to expand background checks for gun buyers gained the backing of one Republican and the potential support of a second on Sunday, along with the support of a prominent gun rights organization. Sponsors said the vote expected this week on the bill was too close to call.
The plan would ‘‘strengthen the background check system without in any way infringing on Second Amendment rights,’’ Senator Susan Collins of Maine said in a statement explaining her support for the measure. But she added that ‘‘it is impossible to predict at this point’’ what will be in a final bill.
Senator John McCain of Arizona, who has a B+ rating from the National Rifle Association, said he was ‘‘very favorably disposed’’ to the proposal that has emerged from Senators Patrick Toomey, Republican of Pennsylvania, and Joe Manchin, Democrat of West Virginia.
‘‘I appreciate their work,’’ McCain said on CNN’s “State of the Union.’’ ‘‘And the American people want to do what we can to prevent these tragedies. And there’s a lot more that needs to be done, particularly in the area of mental health.’’
It was in McCain’s home state that a gunman with schizophrenia shot Gabrielle Giffords, then a member of the House, in the head during a 2011 rampage in Tucson that left six people killed.
Collins and Senator Mark Kirk of Illinois are the only Republicans besides Toomey who are expected to vote for the compromise as of now.
It will take 60 votes to pass, meaning more Republicans will have to come on board, because some Democrats from gun-friendly states are expected to oppose the measure.
‘‘It’s an open question as to whether or not we have the votes. I think it’s going to be close,’’ Toomey said.
The measure requires background checks for people buying guns at gun shows and online. Background checks currently apply only to transactions handled by the country’s 55,000 licensed gun dealers. Private transactions, such as a sale of a gun between family members, would still be exempt.
Speaking on “Fox News Sunday,’’ Manchin also said that some gun rights groups are now prepared to support the legislation. Manchin quoted Alan Gottlieb, the chairman of the Citizens Committee for the Right to Keep and Bear Arms, as saying that his group has read the bill and likes it.
“They are supporting it now. That is huge,’’ Manchin said. Gottlieb did not respond to a request Sunday to provide more details of the position taken by his group.
Manchin urged lawmakers to read the 49-page proposal. He said it should dispel any misconceptions about infringing on the constitutional right to bear arms.
The senators’ proposal includes language expanding firearms rights by easing some restrictions on transporting guns across state lines, protecting sellers from lawsuits if buyers passed a check but later used a gun in a crime, and letting gun dealers conduct business in states where they don’t live.
‘‘If you are a law-abiding gun owner, you’re going to like this bill,’’ Manchin said.
He acknowledged the vote would be tight. Asked how many votes he thought he had now, Manchin said: ‘‘Well, we’re close. We need more.’’
The compromise, if successful, would be added to broader gun control legislation to strengthen laws against illegal gun trafficking and to slightly increase school security aid.
Other additions to the legislation also are expected to be debated this week, including a measure that would allow concealed handgun permits issued by one state to be accepted nationwide as a de facto background check.
Senator Marco Rubio, Republican of Florida, said in news show interviews that concealed weapons permits should be applied nationally. He also called for more prosecution of people who are trying to buy guns and fail a background check.
The Senate is also expected to consider, and reject, Democratic amendments to ban assault weapons and ammunition magazines carrying more than 10 rounds. Votes on the amendments will be held in the days ahead before the Senate considers the overall legislation, which could take weeks.
Senator Kirsten Gillibrand, Democrat of New York, who was involved in crafting the components of the bill that would address gun trafficking and straw purchasing, said on NBC’s “Meet the Press’’ that the overall legislation represented a good compromise between progun rights and progun control lawmakers.